EES-11 - LANL

Regional Phase Amplitude Tomography for Seismic Verification

Tomography Method

Amplitude model:

a_ijk = c_k f(m_bⁱ) s_jk x_ij ^-bk e ^-a_kx_ij,


i, j, k	represent source, site and phase type

c_k      source generation

f       source scaling (taken as known function of m_b)

s_j      site effect

x_ij     distance

b_k      spreading

a_k      spatial attenuation

Take logarithms, correct for source scaling and discretize attenuation:

D_ijk = C_k + S_jk - b_k log₁₀x_ij- log₁₀ e S_m a_km dx_ijm,



m       represents discretization

Form phase ratios:

DD_ij = DC + DS_j - Dblog₁₀x_ij - log₁₀ e S_m Da_m dx_ijm.

Write in matrix form:

Ax = d

Solve using least squares:

x = (A^tW^tWA + S^t L²S)^-1 A^tW^td,



S      represents regularization equations 

L      regularization weights

W      1/data error

Calculate resolution, covariance and prediction error using standard formulae.

Attenuation was discretized using an array of ellipses.

CLICK ON IMAGE TO ENLARGE